How can we convert a decimal number to a binary number?
To convert a decimal number to a binary number, the process involves successive division by 2. The remainders obtained from each division are used to determine the binary representation of the decimal number.
Step-by-Step Process:
1. Start with the decimal number: Begin with the given decimal number that you want to convert to binary.
2. Divide by 2 and record the remainder: Divide the decimal number by 2 and note down the remainder.
3. Repeat the process: Continue dividing the quotient by 2 and recording the remainders until the quotient becomes 0.
4. Read the remainders: The remainders obtained, when read from bottom to top, represent the binary equivalent of the decimal number.
Example:
Let's convert the decimal number 75 to binary using the above process:
- Start with 75.
- 75 divided by 2 gives 37 with a remainder of 1 (rightmost digit).
- Next, 37 divided by 2 gives 18 with a remainder of 1.
- Continuing, 18 divided by 2 gives 9 with a remainder of 0.
- Further, 9 divided by 2 gives 4 with a remainder of 1.
- Then, 4 divided by 2 gives 2 with a remainder of 0.
- Finally, 2 divided by 2 gives 1 with a remainder of 0.
- The binary representation of 75 is 1001011.
By understanding and practicing the conversion process, you can easily convert any decimal number to binary. This knowledge is fundamental in fields such as computer science, where binary numbers are widely used in coding and data representation.